General Navigation - CPL

The PPL navigation lesson covered the grid, directions, the wind triangle and dead reckoning. At CPL level you work over longer distances, where the shape of the Earth matters: great circles, convergency and chart properties, and the planning points that decide whether to continue or turn back.

1. Great circles and convergency

Meridians meet at the poles, so a straight line on the Earth (a great circle) crosses each meridian at a slightly different angle. The change of direction between two meridians is the convergency:

Earth convergency = change of longitude × sin(mean latitude)

Example: from 035°E to 015°E at a mean latitude of 40°N. Change of longitude 20°, sin 40° ≈ 0.64 – convergency ≈ 13°. The great-circle track changes by 13° along the route.
At the equator convergency is zero (meridians are parallel); at the poles it equals the change of longitude.
The conversion angle – the difference between the great-circle and the rhumb-line direction at either end – is half the convergency.
In the northern hemisphere the great circle always lies on the polar side of the rhumb line.

2. Distances on the Earth

Along a meridian: change of latitude in minutes = NM.
Along a parallel: departure = change of longitude (minutes) × cos(latitude).
The Earth's circumference is about 21,600 NM (360° × 60).

3. Chart projections

Projection	Straight line	Scale	Typical use
Mercator	Rhumb line	Correct only at the equator; grows with sec(latitude)	Plotting charts near the equator
Lambert conformal conic	Approximately a great circle	Nearly constant between the standard parallels	Most en-route and VFR charts
Polar stereographic	Approximately a great circle near the pole	Increases away from the pole	Polar navigation

A chart is conformal when angles are shown correctly (shapes are right over small areas). On a Lambert chart, the chart convergency is n × change of longitude, where n = sin(parallel of origin) – it is constant over the whole chart.

4. Scale

Scale = chart distance ÷ earth distance. On a 1:1,000,000 chart, 1 cm = 10 km; on 1:500,000, 1 cm = 5 km. A 10 cm line on a 1:1,000,000 chart is 100 km, or about 54 NM.

5. Time

Local mean time (LMT) differs from UTC by 4 minutes for every degree of longitude: at 36°E, LMT is UTC + 2 h 24 min.
Standard time is the legal time of a country (Jordan UTC+3).
Sunrise and sunset in tables are given in LMT for a latitude; convert to UTC with the longitude. Civil twilight ends when the Sun is 6° below the horizon – night flying rules usually start then.
Crossing the date line westbound you add a day; eastbound you subtract one.

6. Using the navigation computer

The mechanical "whiz wheel" (such as the CRP-5) or its electronic version solves:

The wind triangle: heading and ground speed from track, TAS and wind – or the wind from heading, TAS, track and ground speed.
TAS from CAS, pressure altitude and temperature; density altitude.
Time, speed, distance, fuel and conversions (kg/lb, litres/US gallons, NM/km).

A useful conversion: 1 kg = 2.205 lb, 1 US gallon = 3.785 litres.

7. Equal time point and point of no return

Over sea, desert or remote areas, two planning points tell you your options:

The equal time point (ETP, or critical point) is where it takes the same time to continue to the destination as to return to the departure point. Distance to the ETP = total distance × GS home ÷ (GS out + GS home).
The point of no return (PNR) is the furthest point from which you can still return with your safe endurance. Time to PNR = endurance × GS home ÷ (GS out + GS home).

Example: 600 NM leg, TAS 200 kt, 40 kt headwind outbound (GS out 160, GS home 240). ETP = 600 × 240 ÷ 400 = 360 NM from departure. With 4 hours of safe endurance, time to PNR = 4 × 240 ÷ 400 = 2.4 h, so the PNR is 2.4 × 160 = 384 NM out.

With a headwind outbound, the ETP moves towards the destination – the wind helps you on the way back.

8. Grid and polar navigation (overview)

Near the poles, meridians converge so fast that true directions change quickly along a straight track. Grid navigation lays a square grid over the chart, aligned with one reference meridian, so that a straight line keeps a constant grid track. Airliners crossing high latitudes also switch their heading reference from magnetic to true.

Flying it at Levant

Long Levant routes – Amman to Toronto, Baghdad to East Asia – follow great circles: look at how the initial track on the OFP differs from a straight line on a flat map, and check the ETPs SimBrief prints for oceanic or desert stretches. Knowing where your ETP is tells you which way to turn if something goes wrong.

Check yourself

Change of longitude 30°, mean latitude 30°N. What is the convergency? 30 × 0.5 = 15°.
What is the conversion angle for that leg? 7.5° (half the convergency).
Which projection shows a rhumb line as a straight line? Mercator.
1,000 NM leg, GS out 250 kt, GS home 350 kt. Where is the ETP? 1,000 × 350 ÷ 600 ≈ 583 NM from departure.
What is the local mean time at 45°E when it is 12:00 UTC? 15:00 LMT.

Simulation training material based on standard commercial navigation theory.